Solve xquad6x^2+5x=4

$$x \quad 6 x ^ { 2 } + 5 x = 4$$

Solve for x_6

$$x_{6}=-\frac{5x-4}{x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Subtract 5x from both sides.

$$x_{6}x^{2}=4-5x$$

The equation is in standard form.

$$x^{2}x_{6}=4-5x$$

Divide both sides by x^{2}.

$$\frac{x^{2}x_{6}}{x^{2}}=\frac{4-5x}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$x_{6}=\frac{4-5x}{x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{16x_{6}+25}-5}{2x_{6}}\text{; }x=-\frac{\sqrt{16x_{6}+25}+5}{2x_{6}}\text{, }&x_{6}\neq 0\\x=\frac{4}{5}=0.8\text{, }&x_{6}=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{16x_{6}+25}-5}{2x_{6}}\text{; }x=-\frac{\sqrt{16x_{6}+25}+5}{2x_{6}}\text{, }&x_{6}\neq 0\text{ and }x_{6}\geq -\frac{25}{16}\\x=\frac{4}{5}=0.8\text{, }&x_{6}=0\end{matrix}\right.$$